Rendering an object through another
I believe it can be done. First thing first being setting up the eye material to be visible front side only. (How can I make a material only apply to a side of a plane?)

Next step is constructing a mask from both head and hair using object index passes (How to use an object as a mask?). Using this as a mask for the eyes results that the eyes will become occluded behind other solid objects, like Link's hands.